Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Topic Video
Question
In parallelogram DEFG, what is the EY?
![In the given problem, we have a parallelogram, DEFG, with diagonals that intersect at point Y. The problem asks to find the length of EY.
The diagram is a kite-shaped four-sided figure with the following details:
1. **DG and EF are diagonals:**
- DG = 5x - 5
- EF = 3x + 9
- DY = 4x - 3
2. **Diagonals bisect each other at point Y:**
- In parallelograms, diagonals bisect each other equally. Therefore, DY = YE and GY = YF.
3. **Equations for the line segments:**
- If DY = 4x - 3, then YE should also equal 4x - 3.
To find the values:
1. **Set the segments of equal length:** Since diagonals bisect each other,
\( DG = EF \)
\((5x - 5) + (3x + 9) = 2(4x - 3)\).
2. **Solve for x:**
- Equate the expressions for the diagonals:
\[ 5x - 5 = 4x - 3 \]
- Solve for x:
\[ 5x - 4x = -3 + 5 \]
\[ x = 2 \]
3. **Find EY:**
- Substitute x in DY = 4x - 3:
\[ EY = 4(2) - 3 \]
\[ EY = 8 - 3 \]
\[ EY = 5 \]
Therefore, x = 2 and EY = 5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c2913e4-3d86-4c39-9afb-ae3f41846d68%2F246caf91-818f-41f8-b2ab-1666e118ed0f%2F1tw7cw_processed.png&w=3840&q=75)
Transcribed Image Text:In the given problem, we have a parallelogram, DEFG, with diagonals that intersect at point Y. The problem asks to find the length of EY.
The diagram is a kite-shaped four-sided figure with the following details:
1. **DG and EF are diagonals:**
- DG = 5x - 5
- EF = 3x + 9
- DY = 4x - 3
2. **Diagonals bisect each other at point Y:**
- In parallelograms, diagonals bisect each other equally. Therefore, DY = YE and GY = YF.
3. **Equations for the line segments:**
- If DY = 4x - 3, then YE should also equal 4x - 3.
To find the values:
1. **Set the segments of equal length:** Since diagonals bisect each other,
\( DG = EF \)
\((5x - 5) + (3x + 9) = 2(4x - 3)\).
2. **Solve for x:**
- Equate the expressions for the diagonals:
\[ 5x - 5 = 4x - 3 \]
- Solve for x:
\[ 5x - 4x = -3 + 5 \]
\[ x = 2 \]
3. **Find EY:**
- Substitute x in DY = 4x - 3:
\[ EY = 4(2) - 3 \]
\[ EY = 8 - 3 \]
\[ EY = 5 \]
Therefore, x = 2 and EY = 5.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning